Answer:
4 pencil & 2 ruler = $8
2 pencil & 4 ruler = $10
let the no. of Pencil be X and no. of ruler be Y
4x + 2y = 8
2x + 4y= 10
solving the equation by elimination method,
multiplying eq 2 with 2
4x + 2y = 8
4x + 8y = 20
subtracting,
- 6 y = -12
y = 2
2x + 4(2)= 10
2x + 8 = 10
2x = 10 - 8
2x = 2
x = 1
Cost of 3 ruler + 3 pencil
= 3(1) + 3(2)
= 3 + 6
= 9
= $9Answer:
$9
Step-by-step explanation:
pencil - p
ruler - r
4p + 2r = 8
2p + 4r = 10
4p + 2r = 8 {finding p in terms of r so we can substitiute it}
- 2r -2r
4p = 8 - 2r
÷ 2 ÷2
2p = 4 - r {now, we can replace "2p" in our other equation}
2p + 4r = 10 becomes...
[4 - r] + 4r = 10
4 - r + 4r = 10
4 + 3r = 10
- 4 -4
3r = 6
÷3 ÷3
r = 2
when we have 4 pencils and 2 rulers, we have:
4p + 2[2] = 8
4p + 4 = 8
-4 -4
4p = 4
÷4 ÷ 4
p = 1
{checking with our other equation:
p = 1 ; r = 2
2p + 4r = 10
2[1] + 4[2] = 10
2 + 8 = 10
10 = 10
TRUE STATEMENT;
confirms our variables}
so , we have found that the cost of a pencil is $1, and the cost of a ruler is $2,
p = 1 ; r = 2
so, let's solve our original problem:
3 rulers + 3 pencils = ?
3(2) + 3(1) = ?
6 + 3 = 9
so, the cost of this combination would be $9
hope this helps!! have a lovely day :)
THE
^
Solve: x=4+(4x-4)
O
O
O
x = 2
x = 10
x = 2 or x = 10
Ono real solution
DONE
Answer: x=0
Step-by-step explanation:
[tex]x=4+(4x-4)\\\\x=4+4x-4\\\\x=4x\\\\3x=0\\\\\boxed{x=0}[/tex]
The solution to the equation x = 4 + (x + 4) is 0.
The correct option is "one real solution".
What is an equation?Two algebraic expressions having the same value and symbol '=' in between are called an equation.
Expanding the expression on the right-hand side, we have:
x = 4 + (4x - 4)
x = 4x
Subtracting 4x from both sides, we get:
x - 4x = 0
-3x = 0
Dividing both sides by -3, we get:
x = 0
Therefore, there is one solution to the equation x = 4 + (4x - 4) as the equation simplifies to 0.
So the correct answer is 0, "one real solution".
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At the beginning of a snowstorm, Amadou had 2 inches of snow on his lawn. The snow then began to fall at a constant rate of 0.5 inches per hour. Assuming no snow was melting, how much snow would Amadou have on his lawn 4 hours after the snow began to fall? How much snow would Amadou have on his lawn after tt hours of snow falling
Answer:
4 inches
Step-by-step explanation:
Given information:
2 inches of snow on the lawnRate of snow falling = 0.5 inches per hourSnow did not meltLet y = height of snow on the lawn
Let t = time in hours
⇒ y = 2 + 0.5t
To find how much snow is on the lawn after 4 hours of snowing, substitute t = 4 into the found equation and solve for y:
⇒ y = 2 + 0.5(4)
⇒ y = 2 + 2
⇒ y = 4 inches
Therefore, Amadou will have 4 inches of snow on his lawn after 4 hours of snow falling.
After 4 hours of continuous snowfall at a rate of 0.5 inches per hour, Amadou would have 4 inches of snow on his lawn. After t hours of snow falling at the same rate, he would have 2 + 0.5t inches of snow on his lawn.
After 4 hours of snow falling at a constant rate of 0.5 inches per hour, Amadou would have:
Snow accumulation = Initial snow + (Snowfall rate × Time)
Snow accumulation = 2 inches + (0.5 inches/hour × 4 hours)
Snow accumulation = 2 inches + 2 inches
Snow accumulation = 4 inches of snow.
After t hours of snow falling, the amount of snow on Amadou's lawn would be:
Snow accumulation = Initial snow + (Snowfall rate × Time)
Snow accumulation = 2 inches + (0.5 inches/hour × t hours)
Snow accumulation = 2 + 0.5t inches of snow.
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Does this graph show a function explain how you know
The correct option is Option D: Yes, the graph passes the vertical line test.
The function is a relationship between two distinct sets X and set Y which can be many-one or one-one. here set X is called the domain and set Y is called the codomain.
The vertical line test states that
If we draw a straight vertical line( which is also parallel to the y-axis) and it touches the graph at only one point at all locations, then that relation is said to be a function and this relation will be also one-one.
So here in this function shown in the graph.
If we draw a vertical line parallel to the y-axis in this at any location then it crosses the graph only once. So, it passes vertical line test. And this graph is a function. Therefore option D is correct.
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Use the Pythagorean Theorem to find the length of the leg in the triangle shown below.
The figure shows a right triangle with one leg marked 12. The hypotenuse is marked 15.
Answer:
9
Step-by-step explanation:
a^2+b^2=c^2
a^2+12^2=15^2
a^2=225-144
a=sqrt(81)
a=9
Shawn is collecting money from students at his school for a charity. The table gives the ratios of the number of students who have donated and the amount of money he has collected from them. Complete the table to form equivalent ratios.
In order of blank boxes going from left to right then down will be 1, 9, 5, 75, 35.
The missing table is given below.
What are ratio and proportion?A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.
Shawn is collecting money from students at his school for a charity.
The table gives the ratios of the number of students who have donated and the amount of money he has collected from them.
Since 30 is 1/3 of 90, we know the ratio is 1:3.
In order of blank boxes going from left to right then down
1, 9, 5, 75, 35
The complete table is attached below.
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7. A bag of M&Ms is dumped on the table and you count 82 blue pieces. Approximately how many M&Ms do you expect to be in the entire bag based on the proportions of the entire class? Round to nearest whole M&M
Show calculation and answer
The expected number of M&M's in the bag is 308
How to determine the number of blue pieces?The parameters that complete the question are:
Number of blue pieces = 4
Total = 15
From the question, the number of blue pieces is:
Blue = 82
Let the total number of M&M be M.
So, we have:
Blue = Number of blue/Total * M
This gives
82 = 4/15 * M
Multiply both sides by 15/4
15/4 * 82 = M
Evaluate
M = 307.5
Approximate
M = 308
Hence, the expected number of M&M's in the bag is 308
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6. Five years ago, Ross was N times as old as
Amanda was. If Amanda is now 19 years old,
how old is Ross now in terms of N?
Answer:
14N+5
Step-by-step explanation:
Five years ago; Rose Nx
Amanda x
Now; Rose Nx+5
Amanda x+5=19
x=19-5=14years
Rose(NOW) =14N+5
if n × 18 = ½ find n
Answer:
n = [tex]\frac{1}{36}[/tex]
Step-by-step explanation:
n × 18 = [tex]\frac{1}{2}[/tex]
To find the value of n we have to divide both sides by 18.
Let us solve it now.
18n = [tex]\frac{1}{2}[/tex]
[tex]\frac{18n}{18}[/tex] = [tex]\frac{1}{2}[/tex] ÷ 18
n = [tex]\frac{1}{2}[/tex] ÷ 18
n = [tex]\frac{1}{2}[/tex] ÷ [tex]\frac{18}{1}[/tex]
n = [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{18}[/tex]
n = [tex]\frac{1}{36}[/tex]
A sub sandwich shop offers 12 toppings to choose from. How many ways could a person choose a 4-topping sandwich?
HELPPPPPP
Using the combination formula, it is found that there are 495 ways to choose a 4-topping sandwich.
The order in which the toppings are chosen is not important, hence the combination formula is used to solve this question.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
4 toppings are chosen from a set of 12, hence the number of ways is given by:
[tex]C_{12,4} = \frac{12!}{4!8!} = 495[/tex]
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crash test results the insurance institute for highway safety crashed the 2010 ford fusion four times at 5 miles per hour. the costs of repair for each of the four crashes were $2529,$1889,$2610,$1073 $2529,$1889,$2610,$1073
compute the mean, median, and mode cost of repair.
Answer:
We know that
The costs of repair for each of the four crashes were
$2529, $1889, $2610, $1073
Here we have to compute the mean, median, and mode cost of repair.
Mean = total cost
the no of crashes
Mean = $2529 + $1889 +$2610 +$1073
4
Mean = $2025.25
Therefore the mean = 2025.25
Then we have to find median.
Now first we have to arrange the data in ascending order (smallest to highest).
$1073,$1889,$2529,$2610
Add the two middle numbers and then divide by two, to get the average:
$1889+$2529 = $4418
Median = $4418/2 = $2209
Therefore the median = $2209
Here there is no mode cost.
Which functions have a vertex with a x-value of 0? Select three options.
f(x) = |x|
f(x) = |x| + 3
f(x) = |x + 3|
f(x) = |x| − 6
f(x) = |x + 3| – 6
Answer:
f(x) = |x|f(x) = |x| + 3f(x) = |x| − 6Answer:
A,B,D
Step-by-step explanation:
need help with this question
The local maximum of the equation y = x³ - 5x + 2 is y = 6.3 which occurs at x = -1.29
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the equation:
y = x³ - 5x + 2
The maximum is at dy/dx = 0, hence:
3x² - 5 = 0
x = -1.29 or x = 1.29
y = (-1.29)³ - 5(-1.29) + 2 = 6.3
The local maximum of the equation y = x³ - 5x + 2 is y = 6.3 which occurs at x = -1.29
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[15 PTS] PLS HELP!!!
What is the end behavior of the function?
The correct answer is the fourth option.
5. Identify the sign of the leading coefficient and describe the end behaviour. Using this
information, decide if each function is cubic or quartic.
The sign of the leading coefficient can be found using the graph of a polynomial function.
What is polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
We have given the graph of polynomial functions:
In the first graph:
The leading coefficient is positive.
x → ∞, f(x) → ∞
x → -∞, f(x) → -∞
Degree of a function = 3
In the second graph:
The leading coefficient is negative.
x → ∞, f(x) → -∞
x → -∞, f(x) → -∞
Degree of a function = 4
In the third graph:
The leading coefficient is positive.
x → ∞, f(x) → ∞
x → -∞, f(x) → ∞
Degree of a function = 4
In the fourth graph:
The leading coefficient is negative.
x → ∞, f(x) → -∞
x → -∞, f(x) → ∞
Degree of a function = 3
Thus, the sign of the leading coefficient can be found using the graph of a polynomial function.
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Please SHOW THE WORK. How many miles are in 10 kilometers?
A surgery has a success rate of 75%. Suppose that the surgery is performed on 4 patients. What is the probability that the surgery is successful on exactly 3 patients?
0.21094 is the probability that the surgery is successful on exactly 3 patients.
What is probability?
It is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
According to the given question,
Let Y = The number of patients who respond yes: [tex]Y - Bin (n,p)[/tex]
Given , [tex]n = 4 , p = 0.75 , q = 1 - p = 0.25[/tex]
[tex]P (Y = 3) = \left(\begin{array}{ccc}4\\3\\\end{array}\right) (0.75)^{2}(0.25)^{4-3} \\ = 0.21094\\\\[/tex]
The probability that the surgery is successful on exactly 3 patients is 0.21094
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One person ran 4 miles in 24 minutes. At this rate, how long would it take to run 26 miles?
can i charge my hp laptop more than 1000 times
On Sunday, there were 22 inches of snow. The weather finally began to warm up and by Monday afternoon there were 19 inches. Then on Tuesday, there were 16 inches. If the snow continues to melt the same number of inches every day complete the equation to model the snowmelt if d represents the number of days after Sunday.
Answer:
22-3d=x
Step-by-step explanation:
where d is the days that it melts and the amount of snow x is the snow that is left.
determine domain and range from graph
Domain: (-∞,∞)
Range: (-∞,-3]
Step-by-step explanation:
A quadratic equation graphs a parabola. Therefore there will be arrows on the bottom of the graph as it will go down forever. The domain (min x-values to max x-values) is
(-∞,∞) because the graph keeps on going down and to the right and left. The range (min y-values to max y-values) is (-∞,-3] because the lowest y-value the graph goes to is -∞ nd the highest y-value is -3.
the answer to this question
Each of the integers 1-25 is written on an individual card and placed in a hat. You
randomly draw a card. How many favorable outcomes are there for choosing a card
with an odd number?
Ο Α. 2
OB. 11
O C. 13
OD. 25
Answer:
Step-by-step explanation:
Comment
If you know this formula
tn = t1 + (n - 1)*d then you don't even have to count how many odd numbers there are. If you don't know the formula, then you have to count how many odds there are between 1 and 25 inclusive. Just to save you the trouble, there are 13.
Givens
1 = t1
25 = tn
d = 2
Solution
25 = 1 + (n - 1)*2 Subtract 1 from both sides?
25-1 = 1-1 + (n - 1)*2 Combine
24 = (n - 1) * 2 Divide by 2
24/2 = (n - 1)*2/2
12 = n - 1 Add 1 to both sides
12 + 1 = n - 1 + 1 Combine
13 = n
Answer
So you have 13 cards that will bring success.
What are the zeros of the quadratic function f(x)=6x^2+12x-7?
The zeroes of the quadratic function f(x) = 6x² + 12x – 7 will be given below. Then the correct option is A.
What is a quadratic function ?The quadratic function is given as ax² + bx + c = f(x).
For finding the zeroes of the polynomial we have to find the roots of the polynomial , The value of f(x) = 0
The given function is f(x) = 6x² + 12x – 7
Then the zeroes of the quadratic function will be
[tex]roots = \dfrac {-b \pm \sqrt{b^2 -4ac}}{2a}\\\\[/tex]
Here a =6 , b = 12 ,c = -7
Therefore the zeroes are
[tex]\rm roots = \dfrac {-12 \pm \sqrt{12^2 -4 * 6 * (-7)}}{2 *6}\\\\[/tex]
[tex]\rm root_1 = -1 + \sqrt{\dfrac {13}{6}}\\\\\rm root_2 = -1 - \sqrt{\dfrac {13}{6}}[/tex]
Therefore the correct option is A.
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X= ABC+ AB+ ABC Simplify followings
Answer:
X = ABC+ AB+ ABC
X = AB(C+1+C)
X = AB(2C+1)
Christine splits 4/5 pounds of candy with 5 people. What is the unit rate in pounds per person. In simplest form
Answer:
4/25
Step-by-step explanation:
4/5 ÷ 5 = 4/5 × 1/5 = 4/25
You are given that cos(A)=−5/13, with A in Quadrant II, and sin(B)=7/25, with B in Quadrant II. Find cos(A+B). Give your answer as a fraction.
The value of cos(A+B) is 36/325.
What is Trigonometry?The branch of mathematics concerned with specific functions of angles and their application to calculations.
Given:
cos(A)=−5/13
sin(B)=7/25
Now Using identity,
sin²A + cos² A= 1
sin A= √1 - cos² A
sin A = √1- 25/169
sin A= √144/169
sin A= 12/13
Again,
sin²B + cos² B= 1
cos B= √1 - sin² B
cos B = √1- 49/625
cos B= √576/625
cos B= -24/25
Now,
cos (A +B) = cos A cos B - sin A sin B.
= -5/13* (-24/25) - 12/13* 7/25
= 120/325 - 84/325
= 36/325
Hence, the value of cos (A + B) is 36/325.
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Evaluating a piece-wise function. 10 pts
Evaluate and simplify the expression when a=4 and b=-1 5 - 2(a + 3b)/2
Answer:
4
Step-by-step explanation:
We know that [tex]a = 4[/tex] and [tex]b = -1[/tex], as they are given in the problem. All we have to do is plug them into the equation and solve it.
[tex]5 - 2(a + 3b)/2\\ = 5 - 2(4 -3)/2\\= 5 - 1\\= 4[/tex]
urgent help needed algebra 2
The solution of the given equation (x + 5) - ( 2x - 3) = 6 is 2.
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1.
The standard form of a linear equation is of the form Ax + B = 0.
The given equation is;
(x + 5) - ( 2x - 3) = 6
To solve;
(x + 5) - ( 2x - 3) = 6
Distribute the negative;
(x + 5) - 2x + 3 = 6
we need to get the like terms together;
x - 2x + 5+ 3 = 6
-x + 8 = 6
Subtract 8 from both sides, we get;
-x = -2
x = 2
Hence, the solution of the given equation is 2.
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50% of 42 students are girls. How many of the students are girl's
Answer:
21 girls.
Step-by-step explanation:
50% of 42 students are girls.
So 42/2 = 21.
Therefore 21 of the students are girls.
Hope I helped